R £ P
3tfcEMlNG-/Vtf»j, a kind of chifTels, broader thin ordinary, ufed for opening the feams of fhips, before they are caulked. Btan£fey , sNzv. Expof. p. I30.
REFRACTION (Cjcl.) — The Refraclion of the air has many times fo uncertain an influence On the places of cele- itial objects, very remote from the zenith, that wherever Re- fraEiion is concerned, the conckifions deduced from obferva- tions that are much affected by it, will always remain doubt- ful, and too precarious in many cafes to be relied upon. See Dr. Bradley, in Phil. Tranf. N" 485.
REGIMENTAL Bofpital. See the article Hospital, Append.
R'KLN-deer, the Englifh name of the Rangifer, a creature of the deer-kind. Sue the articles Deer and Rangifer, Suppl.
RELL-moufe, the Englifh. name of the white bellied moufe, with a blackiih back, and long body. See the article Glis,
REPRESENTATIVE (Cyd.)— Representative Power,
in metaphyfics, a term introduced by Leibnitz, to fignify that power of the human fou!, by which it reprefents to itfelf the univerfe, according to the fituation of the body jn the u'rii- verfe. See the article Idea, Suppl.
Wolfius calls this power vis reprejentativa, to denote its be- ing an active power, or rather a force actually exerting itfelf. tor he expr-jfly fays, quod vis confsjlat in continue agendi co- naiu. And he thinks that from this principle of a vis repre- fentativa, ©very phenomenon of the human mind may be ac- counted for. See his Phfycholog. Ration. Art. 529. But it may be prcfumed, that many will find this principle too obfeure to be admitted.
When it is faid, that our ideas are reprefentative of things without uf, or of the univerfe ; it may be afked in what fenfe this is to be underftood ? Do they reprefent it i° as a picture docs its original ? or 2 as an effect of a caufe ? or 3 as a fign reprefents the thing fignified ? The firft opinion is exploded in part by Locke and the Cartefians, and totally by Dr. Berkely, lateBifhop of Cioyne. The fecond is admitted by Hobbes, but denied by Leibnitz himfelf, and the idealifts. The third fhould feem to be the opinion of Leibnitz, but he is not fufficiently explicit.
Dr. Berkeley admits ideas to be figns ; but according to him ithey are arbitrary figns, depending on the immediate will of the deity : hence the vifual language j and ideas, only fig- nify or fuggeft each other, and (pints ; but not bodies, the
- existence of which is totally unknown.
REMITTENTS, or Remitting/ti^H', the fame with the bilious ones. See the article Bilious, Append.
REMOTION, Ranotio, in rhetoric. See the article Meta- stasis, Suppl.
REPETEND, in arithmetic, is ufed for that part of an inter- minate decimal fraction, which is continually repeated ad infi- nitum.
Thus in the interminate decimal fraction 317.- 45 316 316 316, &c. the figures 316 are called the Repel end; Cunn, Treat, of Fractions.
Thefe Repetends often arife in the reduction of vulgar frac- tions to decimals, thus 4. = c. 3333, &c. -f = o. 142857 142857, &c. -,\=^o. 090909, &c.
Single Repetend, is -that where one figure only is repeated, as in 0. 333, &c.
Compound Repetend, is that where two or more figures are repeated, as in o. 09 09, &c. or in 0. 142857 142857, &c.
Decimals with Repetends may always be reduced to vulgar ■fractions. For either the Repetend begins with the decimal, or not :
H the Repetend begins with the firft place of decimals, make it the numerator of- a vulgar fraction, and make the denomi- nator confiffc of as many g's as the Repetend has figures, then will this vulgar fraction be equal to. the decimal. Thus, if the Repetend be fingle, as in o. 333 3, the vulgar fraction equal to it will be = J. = $i So if the Repetend be compound, as in 0. 09 09, &c the equivalent vulgar frac- ■ tion will =; °* = fy = _>_. And in like manner o. 142857 142857, &c. = £££§££ = 7- The re;ifon is obvious from this confederation, that the deci- mal a. 333, ore. is = J 6 + t&j 4* T^ 5 , &c. the fum of which by the rule mentioned under Fraction, SappL will . be equal to -^ divided. by j — ^ — ^= f; and fo of the reft.
If the Repetend does not begin with tire firft place of deci- ..naals, but at fome place farther on towards the right, as in_ the.decima] o. 83333, &c - where the Repetend does not begin till the fecond place of decimals, obferue, that o. 83?^
- to ~ r% + rl* ■+ t& + &c s= T 3 - + - x T \ +
, J ,2 + &c. But 7 l- + !V -f&c z=^ = i, as before, therefore the propofed. decimal is .= T s c -f- ^ s x y = x s -
- Thus alfo if the decimal c. 1 27 27, &c. were propofed,
we (ball find it = £ ? 4. _- 5 * T «£ ;j- T y ?2 4. & c . And j.^ + $h* + & c. bLiing — ii. = T V , the decimal will be = ft + & * J- = f s -f., T i„ = .*# = ^ . The reafon of
which is obvious from what \m beep faid-
REP
If may perhaps be worth while to obfervej that if the nume- rator of a vulgar fraction be unity, and the denominator any prime number, except 2 and 5, the decimal equal to the propofed fraction will always be a Repetend, beginning at the firft place of decimals ; and this Repetend muft neeefiarily be a fubmultiple, or an aliquot part of a number exprefled by as many g's 33 the Repetend has figures ; that is, if the Repetend have 6 figures, it will be a fubmultiple of 999999 ; if four figures, it will be a fubmultiple of 9999, &c. From whence it follows, that if any prime number be called p, the feries 9999, &c. produced as far as is neceffary will always be di- viiible by p, and the quotient will be the Repetend of the de- cimal fraction =
P
REPRODUCTION (Cyd.) — It is very well known, that •trees and plants are to be raifed from flips and cuttings, arid, fome late obfervations have fhewn, that there are fome' ani- mals which have the fame property.
The Polype was the firft initance we had of this ; but we had fcarce time to wonder at the difcovery Mr. Trembley had made, when Mr. Bonett difcovered the fame property jri a fpecles of water-worm. See the articles Polype and WA- ter-worm, Suppl,
Amongft the plants which may be rais'd from cuttings, there are fome which feem to poflefs this quality in fo eminent a degree, that the fmalleft portion of them will become a com- plete tree again. Seethe article Plant, Append. It defer ves enquiry, whether or not the great author of na- ture, when he ordained that certain infects as thefe polypes and worms fhould refemble thofe plants in that particular, al- lowed them this power of being reproduced in the fame de- gree j or, -which is the fame thing, whether this Reproduclion will or will not take place in whatever part the worm is cut : In order to try this, Mr. Bonett entered on a courfe of many ex- periments on the water-worms which have this property. Thefe; are,attheircommon growth, fromtwo to three inches long, and of a brownifh colour, with a caft of reddifh. Frorii one of thefe worms he cut off" the head and tail, taking from each extremity only a final] piece of a twelfth of an inch in length* but neither of thefe pieces were able to reproduce what was wanting. They both pcrifhed in about twenty-four hours' ; the tail firft, and afterwards the head. As to the body of the worm from which thefe pieces were feparated, it lived as well as before, and feemed indeed to .fuffer nothing by the lofs, the head-part being immediately used as if the head was thereon, boring the creature's way into the mud. There are, befides this, two other points in which the Reproduclion Will not take place, the one of thefe is about the fifth or fixth rim from the head, and the other the fame diftance from the tail ; and in all probability the condition of the great artery in thefe pnrts Is the caufe of this.
What is find of the want of the reproduilive poWef of thefe parts, relates only to the head and tail ends • for as to the body, it feels very little inconvenience from the.Iofs of what is taken off, and veryfpeedily reproduces thofeftaits. Where then does the principle of life refide in fuch worms, which after having their heads cut off, will have, not only the fame mo- tions, but even the inclinations, that they had before ; and yet this difficulty is very fmall, compared to fevetal others, which at the fame time offer themfelves to our reafon ? Is this wonderful Reproduclion of parts only a natural confe- quence of the laws' of motion, or are there lodged in the body of the creature a chain of minute buds or (hoots, a fort of little embryos already formed and placed in fuch parts where the Reproducl'ions are to begin ? Are thefe worms only mere machines, or, are they like more perfect animals, a fort of compound, the fprings of whofe motions are actu- ated or regulated by a fort of foul ? And if they have them- felves fuch a principle, how is it that this principle is multi- plied and is found in every feparate piece ? Is it to be granted, that there are in thefe worms not a fingle foul (if it is to be fo called) iri each, but that each contains as many fouls as there are pieces capable of reproducing perfect animals ? Are we to believe with Malpighi, that thefeforts of worms are al! heart and brain from one end to the other ? This may be,, but yet if we knew that it was fo, we fhould know in reality but very little the more for knowing it ; and it fe^erhs after ally that in cafes of this kind we are only to admire the works of the great Creator, and fit down in filence. The nice fenfe of feeling in fpiders has been much talked of by naturalifts ; but. it appears that thefe worms have yet
. fome What more furprizing in them in regard to this particu- lar. If a piece of itick, or any other fubftance, be brought near them, they do not ftay for its touching them, but begfn to leap and frifk about, as foon as it comes towards them. Thete want however fome farther experiments to afcertain whether this be realty owing to feeling or to fight; for tho* We can difcover no diftinct organs of fight in thefe creatures, yet they feem affected by the light of the fun or a candle, and always frifk about it in the fame manner at the approach of either ; nay even the moon-light has fome effect upon them.
2M A
